Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get a 360-lb mixture that is 10% protein?
Cornmeal-how many pounds:__________
Soybean meal-how many pounds:______
To determine the number of pounds of each ingredient needed, we can set up a system of equations based on the given information.
Let's assume we need x pounds of soybean meal and y pounds of cornmeal in the mixture.
Given:
1. Soybean meal is 18% protein.
2. Cornmeal is 9% protein.
3. The desired mixture is 360 lbs and has 10% protein.
To solve the problem, we can create two equations based on the protein content and the total weight of the mixture.
Equation 1: Protein Content Equation
The protein content in the mixture is given as:
(0.18 * x) + (0.09 * y) = 0.10 * (x + y)
Equation 2: Weight Equation
The weight equation tells us that the total weight of the mixture is equal to 360 lbs:
x + y = 360
We have a system of two equations with two variables. We can solve these equations simultaneously to find the values of x and y.
Let's rearrange Equation 2 to express x in terms of y:
x = 360 - y
Substitute this expression for x in Equation 1:
(0.18 * (360 - y)) + (0.09 * y) = 0.10 * (360)
Now, simplify and solve for y:
64.8 - 0.18y + 0.09y = 36
Combine like terms:
0.09y = 36 - 64.8
0.09y = -28.8
Divide both sides by 0.09:
y = -28.8 / 0.09
y = 320
Now, substitute the value of y back into Equation 2 to find x:
x + 320 = 360
x = 360 - 320
x = 40
Therefore, you would need 40 pounds of soybean meal and 320 pounds of cornmeal to create a 360-pound mixture that is 10% protein.
Cornmeal - number of pounds: 320
Soybean meal - number of pounds: 40